No, never. Fighting may occur and gerbils and guinea pigs are two completely different species. Gp's are much larger than gerbils and could seriously injure or even kill them even if not intentionally. In addition to the above, the care and cage requirements are totally different for each animal. They eat very different diets and putting them both together on the same diet is a major mistake and could cost one of the animals their life.
Of course they can but only lucky ones can make babies!
Yes they can live together.
Probably not a good idea. The guinea pig may kill the gerbil and not to mention the gerbil can get out of a guinea pigs cage easily.